PMI Certification Formulae Summary

Possible Formulas Used on Project Management Professional Certification Exam Collected by Kristi L. Myers, Rhonda Brittain, Dale Kelly Refined and compiled by Jeanne Henderson and Kevin Burns Updated for PMBOK 2000 by Jeff Harma (changes shown in bold) Time P= pessimistic O=optimistic Activity Duration (t) = optimistic + 4 (most likely) + pessimistic (This is also referred to as the Pert Mean) 6 Activity Duration = Work Quantity / Productivity Rate Standard Deviation (s) = pessimistic-optimistic (This is also referred to as the Pert Standard Deviation) 6 Total Duration (T) = task duration 1, + task duration 2, + task duration 3, +……………task duration n Pert Variance = [O-P / 6]2 Float = Late float – Early Float Communication Number of Communication Paths (or Communication Channels) = Number of people x (Number of people – 1) 2 Risk Statistical Independence: Sum of the Probabilities = 1 When using a decision tree, multiply the percentages on the appropriate branches together to get your probability of that series of events happening. Quality Mode = Most frequent value UCL = Upper control limits LCL = Lower control limits The Variance is the mean of the squares of the deviations of the observations from their mean. The Standard Deviation is the positive square root of the variance. Example: 17, 17, 19, 22 The mode would be 17. Bi-modal: Example: 17, 17, 17, 19, 19, 22 The answer: 17, and 19. Median = Middle value, when all values are in ascending or descending order. If there is an even number of values, take middle two values and divide by 2. _ Mean (x) = Sum of all values / number of values Capacity Index = (UCL – LCL) 6( Standard Deviation (() = Standard Deviation from multiple sources = ( Standard Deviation of sample ( ( ) = ( ( n Variance (var) = (2 Example: Find the variance and standard deviation of the 5 observations 6, 7, 5, 3, 4 (a) First compute the mean. x = 6 + 7 + 5 + 3 + 4 = 25 = 5 5 5 (b) The deviation of any observation x from the mean is the difference x - x , which may be either positive or negative. Use this arrangement to compute the variance: Observation Deviation Squared deviation x x - x (x - x )2 6 6 – 5 = 1 (1)2 = 1 7 7 – 5 = 2 (2)2 = 4 5 5 – 5 = 0 (0)2 = 0 3 3 – 5 = -2 (-2)2 = 4 4 4 – 5 = -1 (-1)2 = 1 Sum = 0 Sum = 10 The sum of the squares of the deviations from the mean is 10., The variance is therefore Variance = sum of squared deviations = 10 = 2 Number of observations 5 (c) The standard deviation is the square root of the variance. · 2 = 1.4 Rule of 7 This means the process is out of control if one of the following is occurring. · Seven points in a row will be on one side of mean =(1/2)7 = 1/128 = .0078 · Seven points in a row will be on one side or other of mean = (1/2)7 + (1/2)7 = 1/64 = .0156 Cost Cost - Earned Value Analysis Acronyms CV = Cost Variance PV = BCWS = Budgeted Cost of Work Scheduled = Planned Value EV = BCWP = Budgeted Cost of Work Performed = Earned Value AC = ACWP = Actual Cost of Work Performed = Actual Cost SPI = Schedule Performance Index CPI = Cost Performance Index SV = Schedule Variance VAC = Variance at Completion BAC = Budget at Completion EAC = Estimate at Completion ETC = Estimate to Complete Formulas Cost Variance CV ($) = BCWP – ACWP = EV - AC Cost Variance CV(%) = BCWP – ACWP x 100 = EV - AC x 100 BCWP EV Total Cost Variance = (Planned Cost per Unit – Actual Cost per Unit) x Actual Units % Complete = BCWP x 100 = EV x 100 BAC BAC % Spent = ACWP x 100 = AC x 100 BAC BAC Cost Performance Index (CPI) = BCWP / ACWP = EV / AC (< 1 = over budget, > 1 = under budget) Schedule Performance Index (SPI) = BCWP / BCWS = EV / PV (<1 = behind schedule, >1 = ahead of schedule) Schedule Variance SV($) = BCWP – BCWS = EV - PV Schedule Variance SV (%) = SV($) / BCWS = SV($) / PV Variance at Completion (VAC) = BAC – EAC Estimate to Complete (ETC) = EAC – ACWP = EAC - AC Estimate at Completion (EAC) = ACWP + (BAC – BCWP) = AC + (BAC - EV) Independent Forecast = ACWP + BAC – BCWP = AC + BAC - EV CPI CPI And look at EAC from the CPI View and the SPI View EAC = (ACWP / BCWP) * BAC = BAC / CPI = (AC / EV)*BAC = BAC / CPI EAC = (BCWS / BCWP) * BAC = BAC / SPI = (PV / EV)*BAC = BAC / SPI Cost Value of Money PVIF = Present Value Interest Factors FV = Future Value i = interest NPV = Net Present Value PV = Present Value __________________________________________________________________________________________ Payback period = Investment / After-tax cash flow (Expressed in $ per period) Defined as the length of time required to recover the first cost of an investment from a net cash flow produced by that investment for an interest rate of zero. Example: Evaluation of Projects V and W Project Investment, $ 1 2 3 4 5 6 Payback Period Years NPV at 10% IRR V 2000 1000 1000 2 467 23.4% W 2000 800 800 800 800 800 800 2.5 1464 32.7% PBP for V = $2000 / $1000 per month = 2 months. Accounting Rate of Return = Annual After-tax Net Income / Investment ___________________________________________________ Net Present Value (NPV) = FV / (1 + i)n or Net Present Value (NPV) = PV of Revenue – PV of Cost _____________________________________________________________________________ NPV annually (PV) = FV / [(1 + i)n + (1 + Iin-1 + (1 + i)n-2……………+ ((1 + I)1] Present Value (PV) = FV / (1 + r) n Where r = interest rate, n = periods Present Value (PV) = FV * PVIF Future Value (FV) = PV * (1 + r)n Where r = interest rate, n = periods Future Value (FV) = PV / PVIF Future Value Annually (FV) = PV x [(1 + i)n + (1 + Iin-1 + (1 + i)n-2……………+ ((1 + I)1] Benefit Cost Ratio (BCR) = PV of Revenue / PV of Cost Expected Monetary Value (EMV) = Outcome x Probability of Outcome Cost - Depreciation Straight line depreciation = (Investment - Salvage) / Number of years Sum of Years Digits (SYD) = (Investment - Salvage) x (Number of Years Remaining / Sum of Years) Double Declining Balance ((DDB) = (Investment or Remainder) x (2 x Straight line %) Cost – Other Fixed Price plus Incentive Fee = Actual Cost + Fixed Fee + Incentive Where Incentive = Over/Underage x Seller’s % For example: A pre-Arranged 30% of $100K overage costs the seller (negative) $30K Another example: 20% of $50K underage nets the seller (positive) an extra $10K IRR = Internal Rate of Return – The discount rate that equates the present value of cash inflows with the initial investment associated with a project, thereby making NPV = 0. The criterion when the IRR is used to make accept-reject decisions is as follows: If the IRR is greater than the cost of capital, accept the project; if the IRR is less than the cost of capital, reject the project. This criterion guarantees that the firm earns at least its required return. Such an outcome should enhance the market value of the fir and therefore the wealth of its owners. The IRR can be found either by using trial-and-error techniques or with the aid of a sophisticated financial calculator or computer. Formula for finding IRR for an Annuity: 1. Calculate the payback period for the project. 2. Use a table (the present-value interest factors for a $1 annuity, PVIFA) to find, for the life of the project, the factor closest to the payback value. The discount rate associated with that factor is the internal rate of return (IRR) to the nearest 1 percent. Estimating Order of Magnitude (-25% to +75%) gross Conceptual Preliminary Definitive (-5% to +10%) most precise Control / Budget / Design / Appropriation (-10 to +25% (other) = ( var ((x - x)2 n ( ((1)2 + ((2)2 + ((2)2 …….+((n)2